Origin of the Correspondence Rules of Quantum Theory

TL;DR

This paper introduces the Average-Value Correspondence Principle, providing a systematic derivation and physical interpretation of the quantum correspondence rules from classical measurement relations.

Contribution

It presents a new physical principle that explains the origin of quantum correspondence rules and clarifies their applicability and interpretation.

Findings

Derivation of all common correspondence rules from the new principle

Provides a clear physical interpretation of the rules

Defines the domain of applicability of the rules

Abstract

To apply the abstract quantum formalism to a particular physical system, one must specify the precise form of the relevant measurement and symmetry transformation operators. These operators are determined by a set of rules, the correspondence rules of quantum theory. The physical origin of these rules is obscure, and their physical interpretation and their degree of generality is presently unclear. In this paper, we show that all of the commonly-used correspondence rules can be systematically derived from a new physical principle, the Average-Value Correspondence Principle. This principle shows that the correspondence rules result from the systematic translation of relations between measurement results known to hold in a classical model of a system, providing these rules with a clear physical interpretation, and clearly demarcating their domain of applicability.